What are the key concepts for solving trigonometric functions?

[sweetcomedygirl]

Let f be the function defined by f(x) = sin(x)^2 - sin(x) for
0 < x < 3π/2
a. Find the x-intercepts of the graph of f.
b. Find the intervals on which f is increasing.
c. Find the absolute maximum value and the absolute minimum value of f.

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I found the x-intercepts to be x=0, π/2, and π, but for part b I know I need to take the derivative of f(x), but I don't know how, and when I tried to do so on my calculator I couldn't decipher the graph that it was showing me.

 

[colby2152]

$$f(x) = sin^2(x) - sin(x)$$
$$f'(x) = 2sin(x)cos(x) - cos(x)$$
$$2sin(x)cos(x) - cos(x) = 0$$
$$cos(x)(2sin(x) - 1) = 0$$
Solve for $$cos(x) = 0$$ & $$sin(x) = 0.5$$

Then you need to test values for all x values that satisfy those equations within the boundary $$0 < x < \frac{3\pi}{2}$$

 

[rebecca]

trig question

I was trying to prove the identity of cos(A+B)= Cos A Cos B - Sin A Sin B, i couldn't do it. Would u be able to direct me step by step to prove that .

 

[EnumaElish]

sweetcomedygirl: in (c), how are abs. min. and abs. max. defined?

rebecca: You can start with the attached figure. Then, you can write sin α/cos α in terms of cos β, sin β, and cos(α+β)/sin α.